I think I've mostly seen this meme on Facebook, but others have posted it to Dreamwidth and so will I.

Matchbox 20, Yourself or Someone Like YouThird Eye Blind, Third Eye Blind [although Blue is now my fave of theirs]Vertical Horizon, Everything You WantBlink-182, Enema of the StateLinkin Park, Hybrid TheoryGreen Day, DookieThe Starting Line, Say It Like You Mean ItFall Out Boy, Take This to Your GraveAlanis Morissette, Jagged Little PillNew Found Glory, Sticks and Stones

ALSO, I might be showing my youth here, but there are a lot of singles I got a hold of through of through a friend or etc. that were super meaningful to me even if I didn't have the full album. Example, Swing Swing by the All-American Rejects, as well as songs by Dashboard Confessional, Switchfoot, Lifehouse, Good Charlotte, Simple Plan, The Ataris, etc.

Soundtracks were also a massive influence on me, probably moreso than half the albums on this list. These would include Les Miz, Everworld, Spider-Man 2, A Walk to Remember, MOULIN ROUGE, etc.